The newly empowered Democrats are likely to have a fractious relationship with the president, do not see eye to eye with many of his policies — and they may try to impeach him.

"I think there could be much clearer tension," said Tom Block, Washington policy strategist at Fundstrat. "They're going to subpoena Trump's tax returns. That could go all the way to the Supreme Court. In the short term, there's going to be no change to the economic policy. The good economy is baked in for the next 12 months and with the divided government, there could be an infrastructure bill."

Stock futures were firmer Tuesday night, but well off highs reached when it looked like Republicans had a chance of holding onto the House. Treasury yields were lower, and the dollar gave up its early evening gains and was lower against the euro.

"It's certainly not the blue wave Democrats were hoping for," said Jack Ablin, chief investment officer at Cresset Wealth Advisors. "Based on what we're seeing right now, the stock market is liking it. History has shown that the mixed party control is generally the best combination. This is as close to market expectations as we're likely to see."

But Ablin also cautioned that Democrats could be tough on Trump. "Is it impeachment or infrastructure?" he said.

"I think it's a disappointing night for the Democrats, certainly in the Senate. It's not a disaster," said Greg Valliere, chief global strategist at Horizon Investments. "One underestimates Donald Trump at one's own peril. He made the Senate his priority, and this looks like a surprisingly strong showing for Republicans in the Senate."

Dan Clifton, head of policy research at Strategas Research, said Trump is motivated to continue driving policies that boost the economy, with his own re-election now in sight.

"Starting tomorrow, the president is going to start thinking about his own election and he's going to see his party struggled a bit in the suburbs," said Clifton.

For that reason, he may try to resolve trade tensions with China, and show some progress when he meets with China President Xi Jinping at G-20 at the end of the month.

"A win is a win, and it's coming in pretty big," said Clifton. "That allows them to stand up there and say we now have a mandate from the American people for oversight of this president and his policies. That kind of starts everything off. [Democrat Rep. Nancy] Pelosi is going to have to figure out what she wants her accomplishment to be. You just can't investigate and beat up. At some point they're going to have to make a decision — results or resistance."

Trump agenda appears intact

While Democrats apparently took the majority in the House, they lost ground in the Senate, according to NBC News. Indiana's incumbent Democratic Sen. Joe Donnelly was projected to lose his seat to GOP challenger Mike Braun. A Republican Senate seat was also added in North Dakota, and incumbent Texas Sen. Ted Cruz won a close race against Democratic upstart Beto O'Rourke, NBC News projected.

"This guarantees the Trump economic agenda remains intact," said Valliere. "The Trump agenda is fully intact with the Senate adding a couple more Republicans. ... It makes it easier to confirm judges. The Republican agenda is alive and well in the Senate."

Block said Democrats in the House will not be able to roll back tax reform, but they will take on issues such as climate change and health care. "They're going have hearings on climate change. They're going to get people with pre-existing conditions and have hearings. They're going to have hearings on all these hot button issues that have been ignored," said Block.

"There's no wave but it's just hard to overstate how important it is to control one part of the government, and the House has no filibuster," he added. "One of the things that's sort of 'inside the beltway' is how powerful a committee chairman is in Congress — the one bastion of true, undiluted power."

But Democrats and Trump may also find common ground, such as in controlling drug prices or increasing infrastructure spending. "If you are a Republican in Congress you might not like the government spending on infrastructure," Block said. "You might not like government taking a position on pharma, but you're not going to fight Trump on those issues."